From The Art and Popular Culture Encyclopedia

Having an existence outside of the natural world. In this sense, everything supernatural is also preternatural

Beyond or different from what is natural or according to the regular course of things; therefore something which is strange; inexplicable; extraordinary; uncommon; irregular; or abnormal. This more limited sense is often used to describe things which are fully in the natural world, but are merely extreme examples

The preternatural or praeternatural is that which appears outside or beyond (Latin præter) the natural. While this may include what is more commonly called the supernatural, it may also simply indicate extremity - an ordinary phenomenon taken 'beyond' the natural. One may have, for example, a preternatural desire, a preternatural curiosity, a preternaturally acute ear (sense of hearing), or even preternaturally big ears.

Often used to distinguish from the divine (supernatural) while maintaining a distinction from the purely natural. For instance, in theology, the angels, both holy and fallen, are endowed with preternatural powers. Their intellect, speed, and other characteristics are beyond human capacities but are still finite.